# Intrepid::Basis_HGRAD_HEX_C2_FEM< Scalar, ArrayScalar > Class Template Reference

Implementation of the default H(grad)-compatible FEM basis of degree 2 on Hexahedron cell. More...

Inheritance diagram for Intrepid::Basis_HGRAD_HEX_C2_FEM< Scalar, ArrayScalar >:

List of all members.

## Public Member Functions

Constructor.
void getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const EOperator operatorType) const
Evaluation of a FEM basis on a reference Hexahedron cell.
void getValues (ArrayScalar &outputValues, const ArrayScalar &inputPoints, const ArrayScalar &cellVertices, const EOperator operatorType=OPERATOR_VALUE) const
FVD basis evaluation: invocation of this method throws an exception.

## Private Member Functions

void initializeTags ()
Initializes tagToOrdinal_ and ordinalToTag_ lookup arrays.

## Detailed Description

### template<class Scalar, class ArrayScalar> class Intrepid::Basis_HGRAD_HEX_C2_FEM< Scalar, ArrayScalar >

Implementation of the default H(grad)-compatible FEM basis of degree 2 on Hexahedron cell.

Implements Lagrangian basis of degree 2 on the reference Hexahedron cell. The basis has cardinality 27 and spans a COMPLETE tri-quadratic polynomial space. Basis functions are dual to a unisolvent set of degrees-of-freedom (DoF) defined and enumerated as follows:

=================================================================================================
|         |           degree-of-freedom-tag table                    |                           |
|   DoF   |----------------------------------------------------------|      DoF definition       |
| ordinal |  subc dim    | subc ordinal | subc DoF ord |subc num DoF |                           |
|=========|==============|==============|==============|=============|===========================|
|    0    |       0      |       0      |       0      |      1      |   L_0(u) = u(-1,-1,-1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    1    |       0      |       1      |       0      |      1      |   L_1(u) = u( 1,-1,-1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    2    |       0      |       2      |       0      |      1      |   L_2(u) = u( 1, 1,-1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    3    |       0      |       3      |       0      |      1      |   L_3(u) = u(-1, 1,-1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    4    |       0      |       4      |       0      |      1      |   L_4(u) = u(-1,-1, 1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    5    |       0      |       5      |       0      |      1      |   L_5(u) = u( 1,-1, 1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    6    |       0      |       6      |       0      |      1      |   L_6(u) = u( 1, 1, 1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    7    |       0      |       7      |       0      |      1      |   L_7(u) = u(-1, 1, 1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    8    |       1      |       0      |       0      |      1      |   L_8(u) = u( 0,-1,-1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|    9    |       1      |       1      |       0      |      1      |   L_9(u) = u( 1, 0,-1)    |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   10    |       1      |       2      |       0      |      1      |   L_10(u) = u( 0, 1,-1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   11    |       1      |       3      |       0      |      1      |   L_11(u) = u(-1, 0,-1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   12    |       1      |       8      |       0      |      1      |   L_12(u) = u(-1,-1, 0)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   13    |       1      |       9      |       0      |      1      |   L_13(u) = u( 1,-1, 0)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   14    |       1      |      10      |       0      |      1      |   L_14(u) = u( 1, 1, 0)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   15    |       1      |      11      |       0      |      1      |   L_15(u) = u(-1, 1, 0)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   16    |       1      |       4      |       0      |      1      |   L_16(u) = u( 0,-1, 1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   17    |       1      |       5      |       0      |      1      |   L_17(u) = u( 1, 0, 1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   18    |       1      |       6      |       0      |      1      |   L_18(u) = u( 0, 1, 1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   19    |       1      |       7      |       0      |      1      |   L_19(u) = u(-1, 0, 1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   20    |       3      |       0      |       0      |      1      |   L_20(u) = u( 0, 0, 0)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   21    |       2      |       4      |       0      |      1      |   L_21(u) = u( 0, 0,-1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   22    |       2      |       5      |       0      |      1      |   L_22(u) = u( 0, 0, 1)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   23    |       2      |       3      |       0      |      1      |   L_23(u) = u(-1, 0, 0)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   24    |       2      |       1      |       0      |      1      |   L_24(u) = u( 1, 0, 0)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   25    |       2      |       0      |       0      |      1      |   L_25(u) = u( 0,-1, 0)   |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|   26    |       2      |       2      |       0      |      1      |   L_26(u) = u( 0, 1, 0)   |
|=========|==============|==============|==============|=============|===========================|
|   MAX   |  maxScDim=2  |  maxScOrd=12 |  maxDfOrd=0  |      -      |                           |
|=========|==============|==============|==============|=============|===========================|

Remarks:
Ordering of DoFs follows the node order in Hexahedron<27> topology. Note that node order in this topology does not follow the natural oder of k-subcells where the nodes are located, except for nodes 0 to 7 which coincide with the vertices of the base Hexahedrn <8> topology. As a result, L_0 to L_7 are associated with nodes 0 to 7, but L_8 to L_19 are not associated with edges 0 to 12 in that order.

Definition at line 124 of file Intrepid_HGRAD_HEX_C2_FEM.hpp.

## Member Function Documentation

template<class Scalar , class ArrayScalar >
 void Intrepid::Basis_HGRAD_HEX_C2_FEM< Scalar, ArrayScalar >::getValues ( ArrayScalar & outputValues, const ArrayScalar & inputPoints, const EOperator operatorType ) const [inline, virtual]

Evaluation of a FEM basis on a reference Hexahedron cell.

Returns values of operatorType acting on FEM basis functions for a set of points in the reference Hexahedron cell. For rank and dimensions of I/O array arguments see Section MD array template arguments for basis methods.

Parameters:
 outputValues [out] - rank-2 or 3 array with the computed basis values inputPoints [in] - rank-2 array with dimensions (P,D) containing reference points operatorType [in] - operator applied to basis functions

Implements Intrepid::Basis< Scalar, ArrayScalar >.

Definition at line 104 of file Intrepid_HGRAD_HEX_C2_FEMDef.hpp.

The documentation for this class was generated from the following files:

Generated on Tue Oct 20 15:10:08 2009 for Intrepid by  1.6.1